Question

Sunflower oil contains 0.080 mol palmitic acid (C16H32O2)/mol, 0.060 mol stearic acid (C18H36O2)/mol, 0.27 mol oleic acid (C18H34O2)/mol, and 0.59 mol linoleic acid (C18H32O2)/mol. To create margarine from sunflower oil, the liquid oleic and linoleic acids are hydrogenated in the presence of a metal catalyst to form solid stearic acid. At a margarine production facility, a stream of 335.0 mol sunflower oil/hr is fed into a reactor. The fresh hydrogen source available is a mixture containing 0.95 mol H2/mol and 0.050 mol N2/mol. (N2 is inert in this process.) To insure complete hydrogenation, the hydrogen gas mixture is introduced into the reactor in 65.0% excess. All reaction products leave the reactor and proceed to a separator where palmitic and stearic acids are separated from the hydrogen gas mixture. The hydrogen gas mixture is recycled to the fresh feed stream, and 140.0 mol gas/hr of this recycle stream is purged to prevent the buildup of nitrogen gas. What is the composition of the purge stream?

Answer 1

`x_H=0.882`

`x_N=0.118`

Step-by-step explanation:

In this reactor, oleic and linoleic acid react with hydrogen to form stearic acid. This reactions can be represented by:

Oleic:
`C_(18)H_(34)O_2 (l) + H_2 (g) \longrightarrow C_(18)H_(36)O_2 (l)`

Linoleic:
`C_(18)H_(32)O_2 (l) + 2 H_2 (g) \longrightarrow C_(18)H_(36)O_2 (l)`

Having this reactions in mind, the first thing is to determine the moles of hydrogen required:

Base of caculation: 1 mol of sunflower oil

For oleic acid:
`n_(Holeic)=(1 mol H_2)/(1 mol oleic)*(0.27 mol oleic)/(1 mol oil)*(335 mol oil)/(hr)`

`n_(Holeic)=frac{90.45 mol H_2}{hr}`

For linoleic acid:
`n_(Hlinoleic)=(2 mol H_2)/(1 mol linoleic)*(0.59 mol linoleic)/(1 mol oil)*(335 mol oil)/(hr)`

`n_(Holeic)=frac{395.3 mol H_2}{hr}`

`n_(Htotal)=(90.45 mol H_2)/(hr)+(395.3 mol H_2)/(hr)`

`n_(Htotal)=frac{485.75 mol H_2}{hr}`

Applying the excess:

`n_(Htotal)=frac{485.75 mol H_2}{hr}*1.65=801.48 mol`

Nitrogen:
`n_N= 801.48 mol*(0.05 mol N)/(0.95 mol)`

`n_N= 42.2 mol N`

After the reactions:

`n_H=801.48 mol-485.75mol=315.73 mol`

and the nitrogen is inert.

Purge stream:

`n_total=42.2+315.73 mol=357.93 mol`

`x_H=(315.73mol)/(357.93mol)=0.882`

`x_N=(42.2mol)/(357.93mol)=0.118`